Franck-Condon factors based on anharmonic vibrational wave functions of polyatomic molecules

Abstract

Franck-Condon (FC) integrals of polyatomic molecules are computed on the basis of vibrational self-consistent-field (VSCF) or configuration-interaction (VCI) calculations capable of including vibrational anharmonicity to any desired extent (within certain molecular size limits). The anharmonic vibrational wave functions of the initial and final states are expanded unambiguously by harmonic oscillator basis functions of normal coordinates of the respective electronic states. The anharmonic FC integrals are then obtained as linear combinations of harmonic counterparts, which can, in turn, be evaluated by established techniques taking account of the Duschinsky rotations, geometry displacements, and frequency changes. Alternatively, anharmonic wave functions of both states are expanded by basis functions of just one electronic state, permitting the FC integral to be evaluated directly by the Gauss-Hermite quadrature used in the VSCF and VCI steps [Bowman et al., Mol. Phys. 104, 33 (2006)]. These methods in conjunction with the VCI and coupled-cluster with singles, doubles, and perturbative triples [CCSD(T)] method have predicted the peak positions and intensities of the vibrational manifold in the X 2B1 photoelectron band of H2O with quantitative accuracy. It has revealed that two weakly visible peaks are the result of intensity borrowing from nearby states through anharmonic couplings, an effect explained qualitatively by VSCF and quantitatively by VCI, but not by the harmonic approximation. The X 2B2 photoelectron band of H2CO is less accurately reproduced by this method, likely because of the inability of CCSD(T)/cc-pVTZ to describe the potential energy surface of open-shell H2CO+ with the same high accuracy as in H2O+.

Anharmonic vibrational frequencies and vibrationally-averaged structures of key species in hydrocarbon combustion: HCO+, HCO, HNO, HOO, HOO–, CH3 +, and CH3

“…Some of these works are based on QFF in tailored coordinates, vibrational perturbation theories including Coriolis coupling, and various CBS extrapolations of electronic energies, including small electronic effects such as core correlation and relativistic effects as well as diagonal Born-Oppenheimer corrections. In contrast to these previous high-accuracy studies, this study and a few previous ones [5][6][7] from our group aim at establishing blackbox computational procedures for low-lying anharmonic vibrational frequency calculations applicable generally and unambiguously to various polyatomic molecules in the same sense of 'model chemistry' advocated by Pople (see, e.g., [45]) in electronic structure theory. The reliance on normal modes, the mixed use of QFF, grid, and hybrid QFF/grid PES representations, and the open-ended combinations of systematic electronic and vibrational many-body methods in this work are to achieve good balance between general applicability of the theories, robustness and availability of the implementations, and high (if not the highest) accuracy.…”

“…Combined with systematic basis sets such as the ones developed by Dunning and co-workers [3,4], they can now routinely predict the electronic properties of small but general polyatomic molecules within controlled accuracy. The objective of this study as well as several recent ones in our group [5][6][7] is to extend the domain of predictive computing to bound nuclear motions, i.e. anharmonic molecular vibrations, vibrationallyaveraged properties, and various molecular spectra.…”

Performance of density functional theory in computing nonresonant vibrational (hyper)polarizabilities

“…Due to a large effort by several groups, however, the prominent role of the vibrational term in many instances is now well‐established. Taking into account the coupling of electronic and nuclear degrees of freedom is necessary not only for resonant processes such as two‐photon absorption, simulation of vibronic profiles and modeling of vibrational sum‐frequency generation spectra, but for non‐resonant processes as well, which is the subject of this article.…”

A variational approach for calculating Franck-Condon factors including mode-mode anharmonic coupling

“…However, to our knowledge, the practical application of these procedures has, thus far, been limited to chemical systems with a maximum of four atoms ͑i.e., six vibrational degrees of freedom͒. [20][21][22] We have recently formulated and implemented an alternative approach [23][24][25] including Duschinsky rotations and anharmonicity ͑including nondiagonal mode-mode coupling͒. It has been successfully applied to ClO 2 , ethylene, 24 and furan, 25 even though the latter molecule has 21 vibrational degrees of freedom.…”

“…16 Accounting for the effect of anharmonicity in the initial and final electronic states PES dramatically increases the computational cost, and in addition, usually requires a more complex formulation. Recently, several new procedures to include anharmonicity have been formulated, [17][18][19][20] allowing the accurate reproduction of experimental spectra for small molecules. However, to our knowledge, the practical application of these procedures has, thus far, been limited to chemical systems with a maximum of four atoms ͑i.e., six vibrational degrees of freedom͒.…”